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lfunc_lfunctions • Show schema
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{'Lhash': '1658191355118218809982158027398', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 12.0], 'a6': [0, 0], 'a7': [0, -5.196152422706632], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.48882512247996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '432.431', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '405785906899961885078897361683', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -12.0], [-125.0, 0]], [[1.0, 0], [0, 5.196152422706632], [-343.0, 0]], [[1.0, 0], [62.353829072479584, 0], [1331.0, 0]], [[1.0, 0], [-7.0, 0], [2197.0, 0]], [[1.0, 0], [0, 84.0], [-4913.0, 0]], [[1.0, 0], [0, 67.54998149518622], [-6859.0, 0]], [[1.0, 0], [-62.353829072479584, 0], [12167.0, 0]], [[1.0, 0], [0, -168.0], 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'8.951704090957151616435704693035942', '10.19543368508928378180129719152595', '10.76338573240326293168378050100185'], 'prelabel': '2-432-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0486458701794446, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30808233342821433754334649053', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75428789836025601458375383294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23720208086741363136866149753', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.48882512247996, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/4/c/g/431/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-432-12.11-c3-0-14', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-432-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0486458701794446, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30808233342821433754334649053', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1658191355118218809982158027398', 'Lhash_array': ['1658191355118218809982158027398'], 'label': '2-432-12.11-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/4/c/g/431/3'}